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The Formation of Shock Waves in Smooth Solutions

  • A. Majda
Chapter
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Part of the Applied Mathematical Sciences book series (AMS, volume 53)

Abstract

From Corollary 2 of Theorem 2.2 in Chapter 2, we have learned that for smooth solutions u(x,t) of the system of conservation laws,
$$ \frac{{\partial u}}{{\partial t}} + \sum\limits_{j = 1}^N {\frac{\partial }{{\partial {x_j}}}{\mkern 1mu} {F_j}(u){\mkern 1mu} = {\mkern 1mu} 0} ,u(x,0) = {u_0}(x) $$
(3.1)
with initial data, uo ∈ Hs(RN), s > N/2 + 1 or more generally, u0 ∈ H ul S , two precise alternatives occur.

Keywords

Shock Wave Initial Data Compact Support Smooth Solution Nonlinear Wave Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1984

Authors and Affiliations

  • A. Majda
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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